Solve -x^2+4-(x-3)(x+1)-(x+1)

$$- x ^ { 2 } + 4 - ( x - 3 ) ( x + 1 ) - ( x + 1 )$$

Evaluate

$$6+x-2x^{2}$$

Solution Steps

Use the distributive property to multiply x-3 by x+1 and combine like terms.

$$-x^{2}+4-\left(x^{2}-2x-3\right)-\left(x+1\right)$$

To find the opposite of x^{2}-2x-3, find the opposite of each term.

$$-x^{2}+4-x^{2}+2x+3-\left(x+1\right)$$

Add 4 and 3 to get 7.

$$-x^{2}+7-x^{2}+2x-\left(x+1\right)$$

To find the opposite of x+1, find the opposite of each term.

$$-x^{2}+7-x^{2}+2x-x-1$$

Combine 2x and -x to get x.

$$-x^{2}+7-x^{2}+x-1$$

Subtract 1 from 7 to get 6.

$$-x^{2}+6-x^{2}+x$$

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$-2x^{2}+6+x$$

Expand

$$6+x-2x^{2}$$

Solution Steps

Use the distributive property to multiply x-3 by x+1 and combine like terms.

$$-x^{2}+4-\left(x^{2}-2x-3\right)-\left(x+1\right)$$

To find the opposite of x^{2}-2x-3, find the opposite of each term.

$$-x^{2}+4-x^{2}+2x+3-\left(x+1\right)$$

Add 4 and 3 to get 7.

$$-x^{2}+7-x^{2}+2x-\left(x+1\right)$$

To find the opposite of x+1, find the opposite of each term.

$$-x^{2}+7-x^{2}+2x-x-1$$

Combine 2x and -x to get x.

$$-x^{2}+7-x^{2}+x-1$$

Subtract 1 from 7 to get 6.

$$-x^{2}+6-x^{2}+x$$

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$-2x^{2}+6+x$$